That’s currently not possible.
ctrl+D invokes "find_under_expand" command, which shares settings with find/replace panel.
Find panels can be opened with certain settings being set via command arguments (e.g.: "command": "show_panel", "args": {"panel": "find", "reverse": false, "case_sensitive": true}), but the same is not possible for "find_under_expand" command.
It would require the latter one to support arguments such as case_sensitive to override settings from find panel or any other option to control its behavior independently from find panel.
That’s not the first time such a question arises.
Maybe a feature request is already hanging around at https://github.com/sublimehq/sublime_text/issues.